Activist investor Carl Icahn stepped up his attack on eBay Inc. on Monday, accusing the online retailer of overlooking conflicts of interest on its board in what amounts to a broadside against a common practice in Silicon Valley.

Mr. Icahn said two long-serving directors, venture capitalist Marc Andreessen and Intuit Inc. founder Scott Cook, were conflicted because of other business interests. Mr. Icahn, who disclosed a 2.2% stake in...